NOt sure if I have a bad battery or fuel pump is going out on 1999 Ford Mustang Cobra

I store my Mustang an a heated garage from November until may and usually do not start it up during those months. The last 2 years it has been hard to start and this year would not start at all. It turned over but wouldn't start. A hint online said to rap the gas tank and it it starts you need a fuel pump. I did that and it did start. I had to do that on a couple different occasions to get it started. To make a long story short. now it seems that it will start everytime with the battery is at full charge. It is the orininal battery. It is producing abut 12.06 on the test meter. I am wondering if I just am not getting enough from the battery to get everything going. Battery or fuel pump. I'm leaning towards a new battery. What do you think. Thanks very much in advance

12.06 is almost a dead battery, it needs to read at least 12.6 volts. 12.4 is a half dead battery and 12.2 is almost dead, so 12.06 is really, really low. You have done well to get the battery to last for all these years, but it's time, a battery is usually good for about 4-5 years,so yours is amazing. I would start your car at least once a wee and run it for 15-20 minutes to boil off any moisture out of the oil and and get the cooling system hot and circulating. Keep the minimum amount of fuel in the tank, because most fuel today is about 10-15% ethanol, which forms and collects water in your fuel when it sits for say 1-2 weeks, so you want the gas through your tank as much as possible and use a fuel storage stabilizer to help it stay burnable. You can get a fuel stabilizer at a parts store, you know haven't you seen the TV add with the guy in the boat after winter and it won't run because he did not use a fuel stabilizer?

Thank you for this very helpful information. I always knew I should perform better maintaince on it while it is stored. I actually kept a full tank in it so it wouldn't get any moisture in it. And yes it has lasted me longer than any other battery. Only 34,000 miles. Again I will take your information and use it wisely. I appreciate your help Dan

12.6 volts is a fully charged battery even if battery voltage is 12 volts under load the battery may fail or supply insufficient voltage to supply current to the fuel pump and computer ,relays ect.....If it starts each time with a charged battery don't concentrate on the fuel pump. Th battery by age should be replaced any way.Modern fuel goes off/goes stall quickly.